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Fin.lean
/- Copyright (c) 2021 Ivan Sadofschi Costa. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Ivan Sadofschi Costa -/ import Mathlib.Data.Finsupp.Single /-! # `cons` and `tail` for maps `Fin n →₀ M` We interpret maps `Fin n →₀ M` as `n`-tuples of elements of `M`, We def...
AesopUnusedTactic.lean
/- Copyright (c) 2024 Jannis Limperg. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jannis Limperg -/ import Aesop import Mathlib.Tactic.Linter.UnusedTactic set_option linter.unusedTactic true /- The unused tactic linter should not consider tactics unused if they a...
Periodic.lean
/- Copyright (c) 2021 Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury Kudryashov, Alex Kontorovich, Heather Macbeth -/ import Mathlib.MeasureTheory.Measure.Lebesgue.EqHaar import Mathlib.MeasureTheory.Measure.Haar.Quotient import Mathlib.MeasureThe...
Imo2013Q1.lean
/- Copyright (c) 2021 David Renshaw. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: David Renshaw -/ import Mathlib.Algebra.BigOperators.Group.Finset.Powerset import Mathlib.Algebra.Order.Field.Rat import Mathlib.Tactic.FieldSimp import Mathlib.Tactic.Positivity.Basic ...
IsGaloisGroup.lean
/- Copyright (c) 2025 Thomas Browning. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Thomas Browning -/ import Mathlib.FieldTheory.Galois.Basic import Mathlib.RingTheory.Invariant.Defs /-! # Predicate for Galois Groups Given an action of a group `G` on an extension ...
Module.lean
/- Copyright (c) 2020 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison -/ import Mathlib.Algebra.Category.ModuleCat.Monoidal.Basic import Mathlib.Algebra.Category.AlgCat.Basic import Mathlib.CategoryTheory.Monoidal.Mon_ /-! # `Mon_ (ModuleCat ...
Basic.lean
/- Copyright (c) 2021 Rémy Degenne. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Rémy Degenne -/ import Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL1 /-! # Conditional expectation We build the conditional expectation of an integrable function `f` ...
Opposite.lean
/- Copyright (c) 2018 Kenny Lau. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kenny Lau -/ import Mathlib.Algebra.Field.Defs import Mathlib.Algebra.Ring.Opposite import Mathlib.Data.Int.Cast.Lemmas /-! # Field structure on the multiplicative/additive opposite -/ as...
Module.lean
/- Copyright (c) 2018 Kenny Lau. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl, Kenny Lau -/ import Mathlib.Algebra.GroupWithZero.Action.Pi import Mathlib.Algebra.Module.LinearMap.Defs import Mathlib.Algebra.Module.Pi import Mathlib.Data.DFinsupp.Defs ...
GroupCompletion.lean
/- Copyright (c) 2024 Mitchell Lee. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mitchell Lee -/ import Mathlib.Topology.Algebra.GroupCompletion import Mathlib.Topology.Algebra.InfiniteSum.Group /-! # Infinite sums in the completion of a topological group -/ open U...
congrm.lean
import Mathlib.Algebra.Ring.Nat import Mathlib.Data.Fintype.Card import Mathlib.Tactic.CongrM private axiom test_sorry : ∀ {α}, α namespace Tests.Congrm set_option autoImplicit true section docs /-! These are the examples from the tactic documentation -/ example {a b c d : ℕ} : Nat.pred a.succ * (d + (c + a.pr...
Relations.lean
/- Copyright (c) 2025 Oliver Nash. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Oliver Nash -/ import Mathlib.LinearAlgebra.RootSystem.GeckConstruction.Basic import Mathlib.LinearAlgebra.RootSystem.GeckConstruction.Lemmas import Mathlib.Algebra.Lie.Sl2 /-! # Relatio...
Basic.lean
/- Copyright (c) 2021 Luke Kershaw. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Luke Kershaw -/ import Mathlib.CategoryTheory.Adjunction.Limits import Mathlib.CategoryTheory.Limits.Preserves.Shapes.Products import Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproduct...
Maps.lean
/- Copyright (c) 2018 Kenny Lau. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kenny Lau -/ import Mathlib.Data.DFinsupp.Module import Mathlib.RingTheory.Ideal.Operations /-! # Maps on modules and ideals Main definitions include `Ideal.map`, `Ideal.comap`, `RingHom....
Topology.lean
/- Copyright (c) 2022 Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury Kudryashov -/ import Mathlib.Analysis.Complex.UpperHalfPlane.MoebiusAction import Mathlib.Analysis.Convex.Contractible import Mathlib.Analysis.LocallyConvex.WithSeminorms import ...
order.lean
import Mathlib.Data.Matrix.Rank import Mathlib.Tactic.Order example (a b c : Nat) (h1 : a ≤ b) (h2 : b ≤ c) : a ≤ c := by order example (a b c d e : Nat) (h1 : a ≤ b) (h2 : b ≤ c) (h3 : c ≤ d) (h4 : d ≤ e) (h5 : b ≠ d) : a < e := by order example (a b c : Nat) (h1 : a = b) (h2 : b = c) : a = c := by order ...
Basic.lean
/- Copyright (c) 2018 Michael Jendrusch. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Michael Jendrusch, Kim Morrison -/ import Mathlib.CategoryTheory.Monoidal.Cartesian.Basic import Mathlib.CategoryTheory.Monoidal.Functor import Mathlib.CategoryTheory.Limits.Types.S...
vector.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq choice. From mathcomp Require Import fintype bigop fi...
cyclotomic.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq path. From mathcomp Require Import div choice fintype tuple finfun bigop prime. From mat...
PullbackCone.lean
/- Copyright (c) 2018 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison, Markus Himmel, Bhavik Mehta, Andrew Yang, Emily Riehl, Calle Sönne -/ import Mathlib.CategoryTheory.Limits.Shapes.Pullback.Cospan /-! # PullbackCone This file provides AP...
Basic.lean
/- Copyright (c) 2021 Yaël Dillies. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yaël Dillies -/ import Mathlib.Algebra.Group.Embedding import Mathlib.Algebra.Order.Interval.Set.Monoid import Mathlib.Order.Interval.Finset.Defs /-! # Algebraic properties of finset in...
cyclotomic.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq path. From mathcomp Require Import div choice fintype tuple finfun bigop prime. From mat...
MonotoneContinuity.lean
/- Copyright (c) 2021 Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury Kudryashov, Heather Macbeth -/ import Mathlib.Topology.Homeomorph.Defs import Mathlib.Topology.Order.LeftRightNhds /-! # Continuity of monotone functions In this file we prove ...
SMul.lean
/- Copyright (c) 2017 Johannes Hölzl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl, Mario Carneiro, Alexander Bentkamp -/ import Mathlib.Algebra.Algebra.Defs import Mathlib.LinearAlgebra.Basis.Basic /-! # Bases and scalar multiplication This file def...
MinMax.lean
/- Copyright (c) 2019 Minchao Wu. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Minchao Wu, Chris Hughes, Mantas Bakšys -/ import Mathlib.Data.List.Basic import Mathlib.Order.BoundedOrder.Lattice import Mathlib.Data.List.Induction import Mathlib.Order.MinMax import Ma...
Countable.lean
/- Copyright (c) 2023 Dagur Asgeirsson. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Dagur Asgeirsson -/ import Mathlib.CategoryTheory.EssentiallySmall import Mathlib.CategoryTheory.FinCategory.Basic import Mathlib.Data.Fintype.EquivFin import Mathlib.Data.Countable....
TermCongr2.lean
import Mathlib.Tactic.TermCongr import Mathlib.Data.Fintype.Card import Mathlib.Tactic.Ring /-! `congr(...)` tests with heavier imports (`TermCongr` is in `Mathlib/Tactic/Common.lean`) -/ namespace Tests set_option autoImplicit true -- set_option trace.Elab.congr true example [Fintype α] [Fintype β] (h : α = β) : ...
SuppressCompilation.lean
/- Copyright (c) 2023 Sébastien Gouëzel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Alex J. Best, Mac Malone -/ import Mathlib.Init import Lean.Elab.Declaration import Lean.Elab.Notation /-! # Suppressing compilation to executable code in a file or in a section C...
Defs.lean
/- Copyright (c) 2019 Reid Barton. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl, Patrick Massot, Sébastien Gouëzel, Zhouhang Zhou, Reid Barton -/ import Mathlib.Topology.ContinuousMap.Defs import Mathlib.Topology.Maps.Basic /-! # Homeomorphisms This ...
Basic.lean
/- Copyright (c) 2018 Mario Carneiro. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro, Johan Commelin -/ import Mathlib.Algebra.Group.Basic import Mathlib.Algebra.Group.Equiv.Defs import Mathlib.Algebra.Group.WithOne.Defs /-! # More operations on `WithOn...
Coherence.lean
/- Copyright (c) 2021 Markus Himmel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Markus Himmel -/ import Mathlib.CategoryTheory.Monoidal.Free.Basic import Mathlib.CategoryTheory.Discrete.Basic /-! # The monoidal coherence theorem In this file, we prove the monoida...
CompactlyGenerated.lean
/- Copyright (c) 2024 Anatole Dedecker. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Anatole Dedecker, Etienne Marion -/ import Mathlib.Topology.Compactness.CompactlyGeneratedSpace import Mathlib.Topology.Maps.Proper.Basic /-! # A map is proper iff preimage of compa...
interval.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq choice. From mathcomp Require Import div fintype bigo...
NumDen.lean
/- Copyright (c) 2018 Kenny Lau. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kenny Lau, Mario Carneiro, Johan Commelin, Amelia Livingston, Anne Baanen -/ import Mathlib.RingTheory.Localization.FractionRing import Mathlib.RingTheory.Localization.Integer import Mathli...
BaseChange.lean
/- Copyright (c) 2023 Eric Wieser. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Eric Wieser -/ import Mathlib.LinearAlgebra.QuadraticForm.TensorProduct import Mathlib.LinearAlgebra.CliffordAlgebra.Conjugation import Mathlib.LinearAlgebra.TensorProduct.Opposite import...
FundamentalTheorem.lean
/- Copyright (c) 2023 Junyan Xu. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Junyan Xu -/ import Mathlib.RingTheory.MvPolynomial.Symmetric.Defs import Mathlib.RingTheory.MvPolynomial.Tower import Mathlib.Data.Finsupp.Notation import Mathlib.Data.Finsupp.WellFounded ...
interval.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq choice. From mathcomp Require Import div fintype bigo...
Basic.lean
/- Copyright (c) 2017 Johannes Hölzl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl, Kim Morrison -/ import Mathlib.Algebra.BigOperators.Finsupp.Basic import Mathlib.Algebra.BigOperators.Group.Finset.Preimage import Mathlib.Algebra.Group.Indicator impor...
ssrmatching.v
From Corelib Require Export ssrmatching.
algC.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrbool ssrfun ssrnat eqtype seq choice. From mathcomp Require Import div fintype path...
presentation.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq. From mathcomp Require Import fintype finset fingroup morphism. (**********************...
gseries.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq path. From mathcomp Require Import fintype bigop finset fingroup morphism. From mathcomp...
CodiscreteCategory.lean
/- Copyright (c) 2024 Alvaro Belmonte. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Alvaro Belmonte, Joël Riou -/ import Mathlib.CategoryTheory.EqToHom import Mathlib.CategoryTheory.Pi.Basic import Mathlib.Data.ULift import Mathlib.CategoryTheory.Category.Cat import ...
MixedCharZero.lean
/- Copyright (c) 2022 Jon Eugster. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jon Eugster -/ import Mathlib.Algebra.CharP.LocalRing import Mathlib.RingTheory.Ideal.Quotient.Basic import Mathlib.Tactic.FieldSimp /-! # Equal and mixed characteristic In commutative ...
Monotone.lean
/- Copyright (c) 2014 Jeremy Avigad. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jeremy Avigad, Andrew Zipperer, Haitao Zhang, Minchao Wu, Yury Kudryashov -/ import Mathlib.Data.Set.Function /-! # Monotone functions over sets -/ variable {α β γ : Type*} open Equi...
Operations.lean
/- Copyright (c) 2017 Johannes Hölzl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl, Yury Kudryashov -/ import Mathlib.Data.ENNReal.Real /-! # Properties of addition, multiplication and subtraction on extended non-negative real numbers In this file we...
ssrmatching.v
From Corelib Require Export ssrmatching.
CategoryTheory.lean
/- Copyright (c) 2024 Jujian Zhang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jujian Zhang -/ import Mathlib.RingTheory.Flat.Basic import Mathlib.Algebra.Homology.ShortComplex.ModuleCat import Mathlib.Algebra.Category.ModuleCat.Monoidal.Basic /-! # Tensoring with...
Filter.lean
/- Copyright (c) 2017 Mario Carneiro. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro -/ import Mathlib.Order.Filter.Cofinite /-! # Computational realization of filters (experimental) This file provides infrastructure to compute with filters. ## Main d...
HalesJewett.lean
/- Copyright (c) 2021 David Wärn. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: David Wärn -/ import Mathlib.Data.Fintype.Option import Mathlib.Data.Fintype.Shrink import Mathlib.Data.Fintype.Sum import Mathlib.Data.Finite.Prod import Mathlib.Algebra.BigOperators.Grou...
Operations.lean
/- Copyright (c) 2024 Jujian Zhang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jujian Zhang, Jireh Loreaux, Yunzhou Xie -/ import Mathlib.Algebra.Group.Subgroup.Map import Mathlib.Algebra.Module.Opposite import Mathlib.Algebra.Module.Submodule.Lattice import Mathli...
test_guard.v
From mathcomp Require Import all_boot. Set Implicit Arguments. Unset Strict Implicit. Unset Printing Implicit Defensive. Inductive tree := Node { children : seq tree }. Inductive ptree (T : Type) := singleton of T | branch of list (ptree T). (* has *) Fixpoint tree_has (T : Type) (p : pred T) (t : ptree T) : bool :...
Split.lean
import Mathlib.Tactic.Basic example : (α : Type) × List α := by constructor · exact [0,1] -- example : (α : Type) × List α := by -- fsplit -- - exact ℕ -- - exact [0,1]
ShortExact.lean
/- Copyright (c) 2024 Joël Riou. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Joël Riou -/ import Mathlib.Algebra.Homology.HomotopyCategory.ShortExact import Mathlib.Algebra.Homology.DerivedCategory.Basic /-! # The distinguished triangle attached to a short exact se...
Field.lean
/- Copyright (c) 2020 Kenny Lau. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kenny Lau -/ import Mathlib.Algebra.Ring.Action.Basic import Mathlib.Algebra.Field.Defs import Mathlib.Algebra.GroupWithZero.Units.Lemmas /-! # Group action on fields -/ variable {M} [Mon...
Rat.lean
/- Copyright (c) 2019 Johannes Hölzl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl, Mario Carneiro -/ import Mathlib.Algebra.Field.Defs import Mathlib.Data.NNRat.Defs /-! # The rational numbers form a field This file contains the field instance on th...
ClearExcept.lean
import Mathlib.Tactic.ClearExcept set_option linter.unusedTactic false set_option linter.unusedVariables false -- Most basic test example (_delete_this : Nat) (dont_delete_this : Int) : Nat := by clear * - dont_delete_this fail_if_success assumption exact dont_delete_this.toNat -- Confirms that clearExcept doe...
sesquilinear.v
From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq div. From mathcomp Require Import choice fintype tuple bigop ssralg finset fingroup. From mathcomp Require Import zmodp poly order ssrnum matrix mxalgebra vector. (************************************************...
Closure.lean
/- Copyright (c) 2024 Peter Nelson. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Peter Nelson -/ import Mathlib.Data.Matroid.Map import Mathlib.Order.Closure import Mathlib.Order.CompleteLatticeIntervals /-! # Matroid Closure A flat (`IsFlat`) of a matroid `M` is a...
Constructions.lean
/- Copyright (c) 2024 Jireh Loreaux. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jireh Loreaux -/ import Mathlib.Analysis.CStarAlgebra.Module.Defs import Mathlib.Analysis.CStarAlgebra.Module.Synonym import Mathlib.Topology.MetricSpace.Bilipschitz /-! # Construction...
Periodic.lean
/- Copyright (c) 2021 Benjamin Davidson. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Benjamin Davidson -/ import Mathlib.Algebra.Ring.NegOnePow /-! # Periodicity In this file we define and then prove facts about periodic and antiperiodic functions. ## Main defini...
ValMinAbs.lean
/- Copyright (c) 2019 Chris Hughes. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Chris Hughes -/ import Mathlib.Data.ZMod.Basic import Mathlib.Tactic.Linarith /-! # Absolute value in `ZMod n` -/ namespace ZMod variable {n : ℕ} {a : ZMod n} /-- Returns the integer ...
Basic.lean
/- Copyright (c) 2021 Riccardo Brasca. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Riccardo Brasca -/ import Mathlib.LinearAlgebra.FreeModule.Basic import Mathlib.LinearAlgebra.Matrix.StdBasis import Mathlib.RingTheory.Finiteness.Cardinality /-! # Finite and free m...
choice.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq. (**************************************************...
Order.lean
/- Copyright (c) 2017 Johannes Hölzl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl -/ import Mathlib.Algebra.Order.Archimedean.Basic import Mathlib.Algebra.Order.BigOperators.Ring.Finset import Mathlib.Topology.Algebra.InfiniteSum.NatInt import Mathlib...
Bits.lean
/- Copyright (c) 2022 Praneeth Kolichala. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Praneeth Kolichala -/ import Mathlib.Data.Nat.Basic import Mathlib.Data.Nat.BinaryRec import Mathlib.Data.List.Defs import Mathlib.Tactic.Convert import Mathlib.Tactic.GeneralizePr...
EpiMono.lean
/- Copyright (c) 2019 Reid Barton. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Reid Barton, Kim Morrison -/ import Mathlib.CategoryTheory.Opposites import Mathlib.CategoryTheory.Groupoid /-! # Facts about epimorphisms and monomorphisms. The definitions of `Epi` an...
Defs.lean
/- Copyright (c) 2023 Yaël Dillies. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yaël Dillies -/ import Mathlib.Algebra.NoZeroSMulDivisors.Basic import Mathlib.Algebra.Order.GroupWithZero.Action.Synonym import Mathlib.Algebra.Order.Monoid.Unbundled.Pow import Mathlib...
Set.lean
/- Copyright (c) 2022 Yaël Dillies. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yaël Dillies -/ import Mathlib.Algebra.Group.Action.Pointwise.Set.Basic import Mathlib.Algebra.GroupWithZero.Action.Basic import Mathlib.Algebra.GroupWithZero.Action.Units import Mathlib...
ULift.lean
/- Copyright (c) 2024 Joël Riou. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Joël Riou -/ import Mathlib.Topology.Category.TopCat.Basic import Mathlib.Topology.Homeomorph.Lemmas /-! # Lifting topological spaces to a higher universe In this file, we construct the f...
Summable.lean
/- Copyright (c) 2024 Chris Birkbeck. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Chris Birkbeck -/ import Mathlib.Analysis.SpecialFunctions.Complex.LogBounds /-! # Summability of logarithms We give conditions under which the logarithms of a summble sequence is s...
ZMod.lean
/- Copyright (c) 2025 Paul Lezeau. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Paul Lezeau, Oliver Nash, Yaël Dillies -/ import Mathlib.Order.Circular import Mathlib.Order.Fin.Basic import Mathlib.Data.ZMod.Defs /-! # The circular order on `ZMod n` This file defin...
BilinearForm.lean
/- Copyright (c) 2020 Anne Baanen. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Anne Baanen, Kexing Ying -/ import Mathlib.LinearAlgebra.BilinearForm.Properties import Mathlib.LinearAlgebra.Matrix.SesquilinearForm /-! # Bilinear form This file defines the conversio...
NonLocalRing.lean
/- Copyright (c) 2025 Michal Staromiejski. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Michal Staromiejski -/ import Mathlib.Algebra.Ring.Pi import Mathlib.Algebra.Ring.Prod import Mathlib.RingTheory.LocalRing.MaximalIdeal.Basic import Mathlib.RingTheory.Spectrum.Ma...
BoundedLinearMaps.lean
/- Copyright (c) 2018 Patrick Massot. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Patrick Massot, Johannes Hölzl -/ import Mathlib.Analysis.NormedSpace.Multilinear.Basic import Mathlib.Analysis.Normed.Ring.Units import Mathlib.Analysis.NormedSpace.OperatorNorm.Mul ...
order.v
(* (c) Copyright 2006-2019 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat choice seq. From mathcomp Require Import path fintype tup...
LeastGreatest.lean
/- Copyright (c) 2016 Jeremy Avigad. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jeremy Avigad, Mario Carneiro -/ import Mathlib.Algebra.Order.Group.OrderIso import Mathlib.Algebra.Ring.Int.Defs import Mathlib.Data.Nat.Find import Mathlib.Order.Bounds.Defs /-! # Le...
ToMulBot.lean
/- Copyright (c) 2016 Jeremy Avigad. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jeremy Avigad, Leonardo de Moura, Mario Carneiro, Johannes Hölzl -/ import Mathlib.Algebra.Order.GroupWithZero.Canonical import Mathlib.Algebra.Order.Monoid.Unbundled.TypeTags import Ma...
Defs.lean
/- Copyright (c) 2020 Ashvni Narayanan. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Ashvni Narayanan -/ import Mathlib.Algebra.Ring.Subsemiring.Defs import Mathlib.RingTheory.NonUnitalSubring.Defs /-! # Subrings Let `R` be a ring. This file defines the "bundled" s...
Basic.lean
/- Copyright (c) 2019 Kevin Kappelmann. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kevin Kappelmann -/ import Mathlib.Data.Seq.Seq import Mathlib.Algebra.Field.Defs /-! # Basic Definitions/Theorems for Continued Fractions ## Summary We define generalised, simple...
Center.lean
/- Copyright (c) 2020 Kexing Ying. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kexing Ying -/ import Mathlib.Algebra.GroupWithZero.Units.Basic import Mathlib.GroupTheory.Subgroup.Center /-! # The center of a group with zero -/ assert_not_exists Ring /-- For a gro...
Discharger.lean
/- Copyright (c) 2019 Sébastien Gouëzel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sébastien Gouëzel, David Renshaw -/ import Mathlib.Tactic.Positivity.Core import Mathlib.Util.DischargerAsTactic /-! # Discharger for `field_simp` tactic The `field_simp` tactic ...
PiTensorProduct.lean
/- Copyright (c) 2024 Jujian Zhang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Jujian Zhang -/ import Mathlib.LinearAlgebra.PiTensorProduct import Mathlib.Algebra.Algebra.Bilinear import Mathlib.Algebra.Algebra.Equiv import Mathlib.Data.Finset.NoncommProd /-! # T...
AssertNoSorry.lean
/- Copyright (c) 2023 David Renshaw. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: David Renshaw -/ import Mathlib.Init import Lean.Util.CollectAxioms import Lean.Elab.Command /-! # Defines the `assert_no_sorry` command. Throws an error if the given identifier uses...
Defs.lean
/- Copyright (c) 2020 Hanting Zhang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Hanting Zhang, Johan Commelin -/ import Mathlib.Algebra.Algebra.Subalgebra.Basic import Mathlib.Algebra.MvPolynomial.CommRing import Mathlib.Combinatorics.Enumerative.Partition /-! # S...
test_intro_rw.v
From mathcomp Require Import ssreflect ssrfun ssrbool ssrnat. Set Implicit Arguments. Unset Strict Implicit. Unset Printing Implicit Defensive. Lemma test_dup1 : forall n : nat, odd n. Proof. move=> /[dup] m n; suff: odd n by []. Abort. Lemma test_dup2 : let n := 1 in False. Proof. move=> /[dup] m n; have : m = n :=...
Stalks.lean
/- Copyright (c) 2019 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison, Justus Springer -/ import Mathlib.Topology.Category.TopCat.OpenNhds import Mathlib.Topology.Sheaves.SheafCondition.UniqueGluing /-! # Stalks For a presheaf `F` on a topol...
Biproducts.lean
/- Copyright (c) 2020 Kim Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kim Morrison -/ import Mathlib.Algebra.Group.Pi.Lemmas import Mathlib.Algebra.Category.Grp.Preadditive import Mathlib.CategoryTheory.Preadditive.Biproducts import Mathlib.Algebra.Categor...
Sigma.lean
/- Copyright (c) 2017 Mario Carneiro. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro, Yaël Dillies, Bhavik Mehta -/ import Mathlib.Data.Finset.Lattice.Fold import Mathlib.Data.Set.Sigma import Mathlib.Order.CompleteLattice.Finset /-! # Finite sets in a ...
countalg.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq choice. From mathcomp Require Import fintype bigop ss...
Superscript.lean
/- Copyright (c) 2023 Mario Carneiro. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro -/ import Mathlib.Init import Batteries.Tactic.Lint /-! # A parser for superscripts and subscripts This is intended for use in local notations. Basic usage is: ``` loc...
Submodule.lean
/- Copyright (c) 2021 Oliver Nash. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Oliver Nash -/ import Mathlib.Algebra.Lie.Subalgebra import Mathlib.LinearAlgebra.Finsupp.Span /-! # Lie submodules of a Lie algebra In this file we define Lie submodules, we construct ...
Resolution.lean
/- Copyright (c) 2024 Joël Riou. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Joël Riou -/ import Mathlib.CategoryTheory.Localization.LocalizerMorphism /-! # Resolutions for a morphism of localizers Given a morphism of localizers `Φ : LocalizerMorphism W₁ W₂` (i.e....
ReflQuiv.lean
/- Copyright (c) 2024 Mario Carneiro and Emily Riehl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro, Emily Riehl -/ import Mathlib.Combinatorics.Quiver.ReflQuiver import Mathlib.CategoryTheory.Category.Cat import Mathlib.CategoryTheory.Category.Quiv /-...
all_solvable.v
From mathcomp Require Export abelian. From mathcomp Require Export alt. From mathcomp Require Export burnside_app. From mathcomp Require Export center. From mathcomp Require Export commutator. From mathcomp Require Export cyclic. From mathcomp Require Export extraspecial. From mathcomp Require Export extremal. From mat...
bigop.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From HB Require Import structures. From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat seq path. From mathcomp Require Import div fintype tuple ...
Finset.lean
/- Copyright (c) 2022 Eric Wieser, Yaël Dillies, Andrew Yang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Eric Wieser, Yaël Dillies, Andrew Yang -/ import Mathlib.Algebra.Order.Ring.Canonical import Mathlib.Data.Finset.Lattice.Fold import Mathlib.Data.Nat.Cast.Order...
automorphism.v
(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *) (* Distributed under the terms of CeCILL-B. *) From mathcomp Require Import ssreflect ssrbool ssrfun eqtype ssrnat fintype. From mathcomp Require Import finset fingroup perm morphism. (*********************...
Exponential.lean
/- Copyright (c) 2021 Anatole Dedecker. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Anatole Dedecker, Eric Wieser -/ import Mathlib.Algebra.Ring.Action.ConjAct import Mathlib.Analysis.Analytic.ChangeOrigin import Mathlib.Analysis.Complex.Basic import Mathlib.Data.Na...
PrimesCongruentOne.lean
/- Copyright (c) 2020 Riccardo Brasca. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Riccardo Brasca -/ import Mathlib.RingTheory.Polynomial.Cyclotomic.Eval /-! # Primes congruent to one We prove that, for any positive `k : ℕ`, there are infinitely many primes `p` s...